If a car traveled from Townsend to Smallville at an average : GMAT Data Sufficiency (DS)
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# If a car traveled from Townsend to Smallville at an average

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If a car traveled from Townsend to Smallville at an average [#permalink]

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07 Nov 2011, 13:46
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If a car traveled from Townsend to Smallville at an average speed of 40 mph and then returned to Townsend later that evening, what was the average speed for the entire trip?

(1) The trip from Townsend to Smallville took 50% longer than the trip from Smallville to Townsend.
(2) The distance from Townsend to Smallville is 165 miles.

How can the answer be A folks?
[Reveal] Spoiler: OA

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Re: Townsend to Smallville [#permalink]

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07 Nov 2011, 15:03
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enigma123 wrote:
If a car traveled from Townsend to Smallville at an average speed of 40 mph and then returned to Townsend later that evening, what was the average speed for the entire trip?

(1) The trip from Townsend to Smallville took 50% longer than the trip from Smallville to Townsend.
(2) The distance from Townsend to Smallville is 165 miles.

How can the answer be A folks?

Lets distance be x miles between 2 cities (lets say T and S).
From T to S speed = 40 mph so time taken = x/40 hrs
From S to T spees = 60 mph (50% less time) so time taken = x/60 hrs

Total time taken = x/40 + x/60 = x/24 hrs
Total distance travelled = 2x miles

So avg speed = 2x/(x/24) = 48 mph

Instead of x you can solve this by taking 40 miles as distance.

So statement 1 is sufficient.
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Re: Townsend to Smallville [#permalink]

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08 Nov 2011, 09:30
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enigma123 wrote:
If a car traveled from Townsend to Smallville at an average speed of 40 mph and then returned to Townsend later that evening, what was the average speed for the entire trip?

(1) The trip from Townsend to Smallville took 50% longer than the trip from Smallville to Townsend.
(2) The distance from Townsend to Smallville is 165 miles.

How can the answer be A folks?

A couple of basics:
1. Average Speed = Total Distance/ Total Time
2. Average Speed = Weighted Average of different speeds where 'time taken' is the weight
3. If equal distances (say d) are traveled at different speeds, a and b, average speed = 2d/[d/a + d/b] = 2ab/(a+b)
In this case, average speed is independent of 'd', the distance.
4. If speeds a and b are maintained for equal time intervals, say t,
average speed = (at+bt)/2t = (a+b)/2
In this case, average speed is independent of 't', the time interval.

Given: Car travels equal distances. Speed in first case is 40 mph. We need the speed in the second case to get the average speed (given by 2*40*b/(40+b))

(1) Ratio of time in the two cases
T to S: S to T= 3:2
Then ratio of speed in the two cases = 2:3
We know the speed from T to S = 40
Then speed from S to T must be 60
Since we have the value of b (= 60) i.e. the speed while coming back, we can easily find the average speed..
Sufficient.

(2) As we discussed, distance traveled doesn't affect average speed in this case. Not sufficient

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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Director Joined: 29 Nov 2012 Posts: 898 Followers: 14 Kudos [?]: 1045 [0], given: 543 If a car traveled from Townsend to Smallville at an average [#permalink] ### Show Tags 11 Jul 2013, 07:38 If a car travelled from Townsend to Smallville at an average speed of 40 mph and then returned to Townsend along the same route later that evening, what was the average speed for the entire trip? (1) The trip from Townsend to Smallville took 50% longer than the trip from Smallville to Townsend. (2) The route between Townsend and Smallville is 165 miles long. [Reveal] Spoiler: Can someone provide a detailed analysis for statement A. Thanks _________________ Click +1 Kudos if my post helped... Amazing Free video explanation for all Quant questions from OG 13 and much more http://www.gmatquantum.com/og13th/ GMAT Prep software What if scenarios http://gmatclub.com/forum/gmat-prep-software-analysis-and-what-if-scenarios-146146.html Director Joined: 14 Dec 2012 Posts: 842 Location: India Concentration: General Management, Operations GMAT 1: 700 Q50 V34 GPA: 3.6 Followers: 59 Kudos [?]: 1289 [1] , given: 197 Re: If a car traveled from Townsend to Smallville at an average [#permalink] ### Show Tags 11 Jul 2013, 07:48 1 This post received KUDOS fozzzy wrote: [Reveal] Spoiler: Can someone provide a detailed analysis for statement A. Thanks hi, let say distance between T and S be X miles time take to cover from T-S=X/40 statement 1==>time for T-S=1.5(time from S-T) THEREFORE==>X/40=1.5(T) THEREFORE ==>T=X/60 Average speed =total dist/total time ==>total dist=X+X=2X AVG SPEED=2X/(X/40+X/60)=48 HENCE SUFFICIENT. HOPE IT HELPS _________________ When you want to succeed as bad as you want to breathe ...then you will be successfull.... GIVE VALUE TO OFFICIAL QUESTIONS... GMAT RCs VOCABULARY LIST: http://gmatclub.com/forum/vocabulary-list-for-gmat-reading-comprehension-155228.html learn AWA writing techniques while watching video : http://www.gmatprepnow.com/module/gmat-analytical-writing-assessment : http://www.youtube.com/watch?v=APt9ITygGss Last edited by blueseas on 11 Jul 2013, 07:58, edited 1 time in total. Math Expert Joined: 02 Sep 2009 Posts: 36590 Followers: 7092 Kudos [?]: 93355 [2] , given: 10557 Re: If a car traveled from Townsend to Smallville at an average [#permalink] ### Show Tags 11 Jul 2013, 07:55 2 This post received KUDOS Expert's post 3 This post was BOOKMARKED If a car travelled from Townsend to Smallville at an average speed of 40 mph and then returned to Townsend along the same route later that evening, what was the average speed for the entire trip? (1) The trip from Townsend to Smallville took 50% longer than the trip from Smallville to Townsend. Time from T to S 3/2 of that from S to T, thus Speed from T to S 2/3 of that from S to T. Thus speed from S to T = 60 mph. Now, $$(average \ speed)=\frac{(total \ distance)}{(total \ time)}=\frac{2d}{\frac{d}{40}+\frac{d}{60}}$$, where d is the distance between S and T --> d reduces --> we can get the average time. Sufficient. (2) The route between Townsend and Smallville is 165 miles long. We know nothing about the speed from S to T. Not sufficient. Answer: A. Hope it's clear. _________________ Math Expert Joined: 02 Sep 2009 Posts: 36590 Followers: 7092 Kudos [?]: 93355 [1] , given: 10557 Re: If a car traveled from Townsend to Smallville at an average [#permalink] ### Show Tags 11 Jul 2013, 07:56 1 This post received KUDOS Expert's post shaileshmishra wrote: fozzzy wrote: [Reveal] Spoiler: Can someone provide a detailed analysis for statement A. Thanks hi, let say distance between T and S be X miles time take to cover from T-S=X/40 statement 1==>time for T-S=1.5(time from S-T) THEREFORE==>X/40=1.5(T) THEREFORE ==>T=X/60 Average speed =total dist/total time ==>total dist=X+X=2X AVG SPEED=2X/(X/40+X/60)=50 HENCE SUFFICIENT. HOPE IT HELPS Small correction: the average speed would be 48 mph, not 50. _________________ Director Joined: 14 Dec 2012 Posts: 842 Location: India Concentration: General Management, Operations GMAT 1: 700 Q50 V34 GPA: 3.6 Followers: 59 Kudos [?]: 1289 [0], given: 197 Re: If a car traveled from Townsend to Smallville at an average [#permalink] ### Show Tags 11 Jul 2013, 07:59 Bunuel wrote: [] Small correction: the average speed would be 48 mph, not 50. thanks bunuel _________________ When you want to succeed as bad as you want to breathe ...then you will be successfull.... GIVE VALUE TO OFFICIAL QUESTIONS... GMAT RCs VOCABULARY LIST: http://gmatclub.com/forum/vocabulary-list-for-gmat-reading-comprehension-155228.html learn AWA writing techniques while watching video : http://www.gmatprepnow.com/module/gmat-analytical-writing-assessment : http://www.youtube.com/watch?v=APt9ITygGss Senior Manager Joined: 13 May 2013 Posts: 472 Followers: 3 Kudos [?]: 160 [0], given: 134 Re: If a car traveled from Townsend to Smallville at an average [#permalink] ### Show Tags 29 Jul 2013, 11:26 1 This post was BOOKMARKED If a car travelled from Townsend to Smallville at an average speed of 40 mph and then returned to Townsend along the same route later that evening, what was the average speed for the entire trip? Distance/Time = average speed D/T = 40 (1) The trip from Townsend to Smallville took 50% longer than the trip from Smallville to Townsend. We're looking for the total time here. In other words, we want to know the total distance/total time (the distance to and from and the speed to and from) We know that the distance is the same for both trips so that can be represented as 2d. Because we don't know the distance, to find time we will have to get distance/speed = time. Total distance = 2d Total time = time from T to S = time from S to T. Time = distance/speed. We know that the speed from T to S was 50% more than from S to T which means that the speed from S to T was 50% greater (i.e. 40 + 40*.5 = 60MPH) Total Distance/Total Time = total average 2d/([d/40] + [d/60]) = total average 2d/([3d/120 + [2d/120]) = total average 2d/(5d/120) = total average 2d * 120/5d 240d/5d d=48 If we plug 48 into d/t = 40 then we can get a value for t. SUFFICIENT (2) The route between Townsend and Smallville is 165 miles long. We know that the distance is 165 which means that the round trip is 330 miles. The problem is, we are looking for average speed and we have no idea what speed was done on the return trip. INSUFFICIENT (B) GMAT Club Legend Joined: 09 Sep 2013 Posts: 13488 Followers: 576 Kudos [?]: 163 [0], given: 0 Re: If a car traveled from Townsend to Smallville at an average [#permalink] ### Show Tags 19 Nov 2013, 21:29 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ GMAT Club Legend Joined: 09 Sep 2013 Posts: 13488 Followers: 576 Kudos [?]: 163 [0], given: 0 Re: If a car traveled from Townsend to Smallville at an average [#permalink] ### Show Tags 26 Nov 2014, 02:03 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ GMAT Club Legend Joined: 09 Sep 2013 Posts: 13488 Followers: 576 Kudos [?]: 163 [0], given: 0 Re: If a car traveled from Townsend to Smallville at an average [#permalink] ### Show Tags 08 Jan 2016, 05:52 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Intern Joined: 05 May 2016 Posts: 8 Location: India Followers: 0 Kudos [?]: 0 [0], given: 7 If a car traveled from Townsend to Smallville at an average [#permalink] ### Show Tags 06 May 2016, 13:30 VeritasPrepKarishma If a car traveled from Townsend to Smallville at an average speed of 40 mph and then returned to Townsend later that evening, what was the average speed for the entire trip? (1) The trip from Townsend to Smallville took 50% longer than the trip from Smallville to Townsend. (2) The distance from Townsend to Smallville is 165 miles. How can the answer be A folks? mam in this you said Ratio of time in the two cases T to S: S to T= 3:2 how mam? can u explain in bit detail plz? Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7125 Location: Pune, India Followers: 2137 Kudos [?]: 13679 [0], given: 222 Re: If a car traveled from Townsend to Smallville at an average [#permalink] ### Show Tags 07 May 2016, 04:29 The trip from T to S took 50% longer. So if trip from S to T took 2 hrs, the trip from T to S took 50% more that is 50% of 2 hrs more i.e. 1 hour extra. So it took 2+1 hours i.e. 3 hrs. This gives a ratio of 3:2. Time taken from T to S : Time taken from S to T. The actual time taken could be anything. 6 hrs and 4 hrs or 9 hrs and 6 hrs etc. Posted from my mobile device _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: If a car traveled from Townsend to Smallville at an average [#permalink]

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26 Oct 2016, 07:22
Even I used to be confused with this concept but a through reading of speed time concept from magoosh helped me clear my basic flaws in understanding.

Coming to the question:
Speed distance has just one killer concept
s=d/t

Which means s is inversely proportional to time.
now it is given t1=1.5t2
therefore s1 which is inversely proportional will be 2/3s2
s1=40 hence s2=60

Apply the average speed formula 2d/(d/40+d/60)
take d common and cancel it .

Voila! you got the answer

Please give a kudos if you liked my answer.
Re: If a car traveled from Townsend to Smallville at an average   [#permalink] 26 Oct 2016, 07:22
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# If a car traveled from Townsend to Smallville at an average

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